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In this study, a robust model-based fault detection and isolation (FDI) scheme for open-circuit faults is presented for voltage source inverters (VSI) feeding induction motor drives. The actuator faults are modelled with an additive perspective in the non-linear dynamics of the induction motor. In order to obtain a robust observer-based FDI scheme, a bank of non-linear proportional-integral observers is proposed, which allows to identify the DC component of the actuator fault profiles. Hence two residuals in the dq-frame are constructed to isolate the faulty switches in the VSI. The diagnosability and decoupling conditions for additive faults are satisfied by considering only the most common measurements (stator currents and mechanical velocity) in induction motors. In this way, residuals are decoupled from the load torque and operating conditions. Meanwhile, in order to isolate faults related to each switching device, it is suggested a directional residual evaluation which relies on the normalisation of the estimations of the DC terms of the faults profiles. The ideas presented in the study are verified experimentally in a test-bench of 3/4 HP induction motor under variable operating conditions (reference frequency and unknown load torque), and parameter uncertainty induced by a continuous operation of the induction motor.